Mathematical Example: Linear Expansion

Question: The length of a steel rod is 100 m at 20°C. If its length becomes 100.033 m at 50°C then determine the coefficient of linear expansion of steel.

Initial length, l = 100 m

Final length, l2 = 100.033 m

Initial temperature, θ1 = 20°C

Final temperature, θ2 = 50°C

Increase of temperature (θ2 – θ1) = 30K

Increase in length, I2 – I1 = 0.033 m

Coefficient of linear expansion, α = ?


We know,

Coefficient of linear expansion, α = (l2 – l1) / l1 (θ2 – θ1)

0.033m / 100m x 30K

= 11* 10-6 m


Observation: Why a gap is kept at the joining point of two rails of a rail line? 

The rails expand due to heat of the sun or due to heat produced by friction between the wheels and rails while the train runs For this expansion sufficient space is kept between the two rails. If gaps between the rails are not kept, the rail line will bend due to its expansion.